In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel for the proof of his incompleteness theorems.
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He found the incompleteness theorem
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Gödel's incompleteness theorem was a theorem that Kurt Gödel proved about Principia Mathematica, a system for expressing and proving statements of number theory with formal logic. Gödel proved that Principia Mathematica, and any other possible system of that kind, must be either incomplete or inconsistent: that is, either there exist true statements of number theory that cannot be proved using the system, or it is possible to prove contradictory statements in the system.
The answer to this question depends on how easy or difficult the eight questions are. If, for example, the questions were based on Godel's incompleteness theorem it is very likely that nobody could answer them - ever.
No. If you work within its definitions and the rules of logic it is not flawed. There are mathematical statements that you cannot prove to be true or false (Godel's incompleteness theorem), but that is not a flaw.